It owned as much as 92 percent of the company after purchasing the interest of the Federal Reserve Board, which acquired 79.9 percent of AIG in September 2008 in exchange for an $85 billion credit facility needed to enable the company to meet margin calls demanded by holders of credit default swaps issued by the company to ensure mortgage-backed securities.

Later, the Fed and Treasury increased its aid considerably. By May 2009 the Fed and Treasury investment had been raised to $182.5 billion.

Through asset sales, profits and other means, AIG reduced the federal investment, and the Fed sold its shares to Treasury and is in the process of selling off the assets in facilities it created to provide cash to AIG in return for mortgage-backed assets AIG turned over the Fed.

John Nadel, an insurance analyst at Sterne Agee and Leach in New York said the 60-day lock-up expires in the second week of November.

He said most investors expect Treasury to "drip" its remaining 15.9 percent stake out on a daily basis, but added that Benmosche's comments suggest a secondary offering may be more likely.

Nadel said that Sterne Agee Leach believes “a complete exit by Treasury is a clear positive.”

“Not only will it remove the overhang of a large known seller, but it should also free up AIG to adjust management compensation and incentives so as to more clearly align with shareholder interests,” Nadel said.